In this study, we propose a spatial stochastic volatility model in which the latent log-volatility terms follow a spatial autoregressive process. Though there is no spatial correlation in the outcome equation (the mean equation), the spatial autoregressive process defined for the log-volatility terms introduces spatial dependence in the outcome equation. To introduce a Bayesian Markov chain Monte Carlo (MCMC) estimation algorithm, we transform the model so that the outcome equation takes the form of log-squared terms. We approximate the distribution of the log-squared error terms of the outcome equation with a finite mixture of normal distributions so that the transformed model turns into a linear Gaussian state-space model. Our simulation results indicate that the Bayesian estimator has satisfactory finite sample properties. We investigate the practical usefulness of our proposed model and estimation method by using the price returns of residential properties in the broader Chicago Metropolitan area.

中文翻译：

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空间随机波动率模型中的贝叶斯推断：芝加哥房价回报的应用*

在这项研究中，我们提出了一个空间随机波动率模型，其中潜在对数波动率项遵循空间自回归过程。尽管结果方程（均值方程）中没有空间相关性，但为对数波动率项定义的空间自回归过程在结果方程中引入了空间相关性。为了引入贝叶斯马尔可夫链蒙特卡罗 (MCMC) 估计算法，我们对模型进行了转换，以便结果方程采用对数平方项的形式。我们用有限的正态分布混合近似结果方程的对数平方误差项的分布，以便转换后的模型变成线性高斯状态空间模型。我们的模拟结果表明贝叶斯估计量具有令人满意的有限样本特性。